Answer to Question #129736 in Physical Chemistry for raju

Question

. 

If the radius of the first Bohr orbit is r, then the deBroglie wavelength in the third Bohr orbit is

Answer 1

Answer.

The radius of first bohr orbit = r

We know for nth bohr orbit its radius r_n ∝ n²

For, third bohr orbit let, radius be r₃

Then,  (r/r₃) = (1/3)²

r₃ = 9r.

The relation between radius of nth bohr orbit and de broglie wavelength (λ) is

2πr_n = nλ

Then here for third bohr orbit n =3 and radius = 9r

Putting these values,

2π.9r = 3λ

λ = 6πr (Ans.)